Answers
In order to have a function that represents continuous growth, the base value that has a variable as exponent must be the constant value "e":
[tex]\begin{gathered} f(x)=a\cdot b^{cx}\\ \\ b=e \end{gathered}[/tex]Looking at the options, the functions that have this base value are options I and II.
Therefore the correct option is A.
Related Questions
3 3 2. Andrea bought 12 bagels and 10 muffins at the bakery. Of these items, of the bagels were multigrain, and of the muffins were bran muffins. 12a. How many multigrain bagels did Andrea buy? multigrain bagels 12b. How many bran muffins did Andrea buy? bran muffins
Answers
12a)
Since there are 2/3 of multigrain bagels of 12 bagels, we can apply the rule of three:
[tex]\begin{gathered} 12\text{ bagels ----- }\frac{3}{3} \\ x\text{ ---------- }\frac{2}{3} \end{gathered}[/tex]where x denote the multigrain bagels. Then, x is given by
[tex]\begin{gathered} x=\frac{\frac{2}{3}\times12}{\frac{3}{3}} \\ \sin ce\text{ 3/3 is one, } \\ x=\frac{2}{3}\times12 \end{gathered}[/tex]Then, we have
[tex]\begin{gathered} x=\frac{2\times12}{3} \\ x=2\times4 \\ x=8 \end{gathered}[/tex]and the answer is 8 multigrain bagels.
12b)
Similarly, we can apply the rule of three as
[tex]\begin{gathered} 10\text{ muffins ----- }\frac{5}{5} \\ y\text{ ---------- }\frac{3}{5} \end{gathered}[/tex]where y denotes the bran muffins. Then y is given by
[tex]\begin{gathered} y=\frac{\frac{3}{5}\times10}{\frac{5}{5}} \\ \sin ce\text{ 5/5 is one, then} \\ y=\frac{3}{5}\times10 \end{gathered}[/tex]So, we have
[tex]\begin{gathered} y=\frac{3\times10}{5} \\ y=3\times2 \\ y=6 \end{gathered}[/tex]and the answer is 6 bran muffins.
A group of 2414 students were surveyed about the courses they were taking at their college with thefollowing results:1158 students said they were taking Dance.1204 students said they were taking History,1107 students said they were taking Math.426 students said they were taking Math and History.501 students said they were taking Math and Dance.599 students said they were taking History and Dance.214 students said they were taking all three courses.Fill in the following Venn Diagram with the cardinality of each region.MathHistoryгуutIIIV. 214IV.VIIDanceVIII.
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Lets fill the Venn diagram. The intersection zones are the following:
where we can see that 287+214 = 501 students said they were taking Math and Dance, 214+385= 599 students said they were taking History and Dance and 212+214 =426 students said they were taking Math and History.
Lets continue with the remaining zones. Then, the final solution is:
The graph of a logarithmic function is given. Select the function for the graph from the options.
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From the graph given, you can see that the curve cuts the x axis at x = 1. This means that the function of the log to base 5 will be x-1. Hence the fucntion for the graph is expressed as:
[tex]f(x)=\log _5(x-1)[/tex]Hence option C is correct
Note that all you need to do is take the log of the function (x-1) to the base of 5
Write a linear equation of a line that passes (-3,-1) and is perpendicular to the graph of y = 2x+3 in eitherslope-intercept, point-slope, or standard form.
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The general slope intercept form of the line is
y = mx + b
Where m is the slope and b is the y-intercept
So,
For the given equation y = 2x + 3
the slope = m = 2
Now, we need to find the equation of the line which is perpendicular to the given line and pass through the point (-3 , -1 )
The slope of the required line = m' = -1/2
Because the product of the two slopes = -1
so, the equation of the required line will be:
[tex]y=-\frac{1}{2}x+b[/tex]find the value of b using the point (-3 , -1 )
so, when x = -3 , y = -1
[tex]\begin{gathered} -1=-\frac{1}{2}\cdot-3+b \\ -1=\frac{3}{2}+b \\ b=-1-\frac{3}{2}=-\frac{5}{2} \end{gathered}[/tex]So, the equation of the required line:
In slope-intercept form is:
[tex]y=-\frac{1}{2}x-\frac{5}{2}[/tex]in standard form:
Multiply all terms by 2
[tex]\begin{gathered} 2y=2\cdot-\frac{1}{2}x-2\cdot\frac{5}{2} \\ 2y=-x-5 \\ \\ x+2y=-5 \end{gathered}[/tex]Finally, in point - slope form
The slope is -1/2 and the point is ( -3 , -1 )
So, the equation will be:
[tex]\begin{gathered} (y-(-1))=-\frac{1}{2}(x-(-3)) \\ \\ (y+1)=-\frac{1}{2}(x+3) \end{gathered}[/tex]
Find the distance between the two points in simplest radical form.(3, -6) and (-1,1)
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You have the points:
(3, -6)
(-1, 1)
To find the distance between two point knowing the coordinates (x,y) you can use the next formula:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then:
x1 = 3 y1 = -6
x2 = -1 y2 = 1
[tex]d=\sqrt[]{(-1-3)^2+(1-(-6))^2}[/tex][tex]d=\sqrt[]{(^{}-4)^2+7^2}[/tex][tex]d=\sqrt[]{16+49}=\sqrt[]{65}[/tex]To simplify you can factorize the number under the root to know if the number can have a part that has a sqare root, as follow:
As you can see 65 can be writen as (5*13) and as none of those numbers have a perfect square root (whole number) the final answer is:
[tex]d=\sqrt[]{65}[/tex]a circular sinkhole has a circumference of 75.36 m s made the diameter of the sinkhole round to the nearest meter
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We will determine the diameter by using the circumference formula, that is:
[tex]C=2\pi r[/tex]Now, we replace the values and solve for the radius (r):
[tex]75.36=2\pi r\Rightarrow r=\frac{75.36}{2\pi}\Rightarrow r\approx12[/tex]Now, since we know that the diameter of the circle is two times the radius then the diameter is approximately 24 m.
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 7. A(5.-8), B(-2,-10), C(-6, -13). D(-2.1)m(AB) m(CD) Types of Lines
Answers
Tow lines AB and CD are perpendicular to each other if their slope can be related like this:
[tex]m(AB)=-\frac{1}{m(CD)}[/tex]Let's first find the slopes of this lines to see if the formula stated above is
accomplished for this case
The formula of a line has the form:
[tex]y(x)=mx+b[/tex]where m, is the slope of the line
The line AB goes through the points (5,-8) and( (-2,-10)
then, y(5)=-8 for the first point, and y(-2)= -10 for the second one.
then:
y(5)= -8=m*(5)+b
and
y(-2)= -10=m*(-2)+b
if we subtract the first expression from the second one we can get:
-8-(-10)=m*5-m*(-2)+b-b, then:
-8+10=2=5*m+2*m=7*m
Then solving for the line AB, m(AB) equals:
[tex]m(AB)=\frac{2}{7}[/tex]Doing the same for the second line CD that goes through points (-6,-13) and (-2,1), we can find its slope like this:
y(-6)= -13 and y(-2)=1
then:
-13= -6*m+b and 1= -2*m+b
substracting both expressions
-13-1= -6*m - (-2)*m
then:
-14= -4*m
then, for line CD, its slope is:
[tex]m=\frac{-14}{-4}=\frac{-7}{-2}=\frac{7}{2}[/tex]As we can see, m(AC)=2/7 and m(CD)=7/2, then the criteria:
[tex]m(AB)=-\frac{1}{m(CD)}[/tex]it's not being accomplished, so we can say that these lines are not perpendicular,
Now, lines are parallel when they have the same slope value, which isn't true in this case.
We can say that these lines are neither parallel nor perpendicular
what type of sequence is shown: 1,2,4,7,10A) Arithmetic sequenceB) geometric sequence C) neithernote this is not graded its practice
Answers
Given Sequence:
[tex]1,2,4,7,10[/tex]If the sequence is arithemetic sequence the difference between to consicutive elements will be same.
[tex]\begin{gathered} d_1=2-1=1 \\ d_2=4-2=2 \end{gathered}[/tex]Since,
[tex]d_1\ne d_2[/tex]The sequence is not a arithmetic sequence.
If the sequence is a geometric sequence the ratio between two succesive elements will be same.
[tex]\begin{gathered} r_1=\frac{2}{1}=2 \\ r_2=\frac{4}{2}=2_{} \\ r_3=\frac{7}{4}=1.75 \end{gathered}[/tex]Since,
[tex]r_2\ne r_3[/tex]The sequence is not a geometric sequence.
Thus, the correct option is option (C) neither. The sequnce is neither arithmetic sequence nor a geometric sequence.
3. What is the domain of the relation: R = {(8. 7), (8. 9), (10, 11), (12. 14)}
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The set of points we have is:
[tex]R=\mleft\{\mleft(8,7\mright),(8,9),(10,11),(12,14)\mright\}[/tex]Let's remember that a point has the general form (x,y), so that the first value in the parentheses is the x-value, and the second value is the y-value.
The domain is the set of values possible for x. In this case, the domain will be all of the x-values of all of the given points.
Domain: {8, 10, 12}
Answer: {8, 10, 12}
The line with slope m=-3/2 and passing through the midpoint of the line segment connecting (3,-2) and (-1/2,4). Leave in Standard Form.
Answers
Hello there. To solve this question, we'll have to remember some properties about equation of lines and midpoints.
First, given a point (x0, y0), the equation of the line with slope m that passes through this point can be found by the point-slope formula:
[tex]y-y_0=m\cdot(x-x_0)[/tex]The standard form of a line equation is:
[tex]y=mx+b[/tex]Which is the same as the first, when defining:
[tex]b=y_0-m\cdot x_0[/tex]In this case, we need to find the midpoint of a segment in order to find a point of the line we want to determine the equation.
Remember that given two points (x1, y1) and (x2, y2), the midpoint (xM, yM) can be found by taking the mean of the x and y values of the points:
[tex]\begin{gathered} x_M=\frac{x_1+x_2}{2} \\ y_M=\frac{y_1+y_2}{2} \end{gathered}[/tex]Knowing the points (3, -2) and (-1/2, 4), the midpoint of the segment connecting these points have coordinates:
[tex]\begin{gathered} x_M=\frac{3-\frac{1}{2}}{2}=\frac{5}{4} \\ y_M=\frac{-2+4}{2}=1 \end{gathered}[/tex]So the point of the line we want to find the equation if (5/4, 1) and its slope was given: m = -3/2.
We calculate b:
[tex]b=1-\mleft(-\frac{3}{2}\mright)\cdot\frac{5}{4}=1+\frac{15}{8}=\frac{23}{8}[/tex]And the equation of the line is finally:
[tex]y=-\frac{3}{2}x+\frac{23}{8}[/tex]Evaluate each arithmetic series described A1=12, an=33, n=8
Answers
Hello!
With this informations, we have to find the ratio of this sequence, using the formula below:
[tex]\begin{gathered} a_n=a_1+(n-1)\cdot r \\ 33=12+(8-1)\cdot r \\ 33=12+7r \\ 33-12=7r \\ 21=7r \\ r=\frac{21}{7} \\ \boxed{r=3} \end{gathered}[/tex]So, this arithmetic series will be:
[tex]\begin{gathered} a_1=12 \\ a_2=15 \\ a_3=18 \\ a_4=21 \\ a_5=24 \\ a_6=27 \\ a_7=30 \\ a_8=33 \end{gathered}[/tex]To finish, let's calculate the sum of the terms of this sequence using the formula:
[tex]\begin{gathered} S_n=\frac{(a_1+a_n)\cdot n}{2}=\frac{(12+33)\cdot8}{2}=\frac{45\cdot8}{2}=\frac{360}{2}=180 \\ \\ \boxed{S_n=180} \end{gathered}[/tex]Find the product of the two complexnumbers. SHOW ALL WORK.(-4 + 2i)(3 - 7i) What’s the answer for this I am lost and confused it’s for a test please help me
Answers
The multiplication of two complex numbers equals another complex number, we can find it with this formula:
[tex](a+bi)\times(c+di)=(ac-bd)+(ad+cd)i[/tex]From our complex numbers, a= -4, b=2, c=3, d= -7, then replacing these values into the above formula we get:
[tex]\begin{gathered} (-4+2i)\times(3-7i)=(-4\times3-2\times-7)+(-4\times-7+3\times-7)i \\ (-4+2i)\times(3-7i)=(-12-(-14))+(28+(-21))i \\ (-4+2i)\times(3-7i)=(-12+14)+(28-21)i \\ (-4+2i)\times(3-7i)=2+7i \end{gathered}[/tex]Then the product of these complex number equals 2+7i
Hey I need help with my math pretest and I’m confused with the questions they are giving me
Answers
ANSWER
[tex]2.25x+12.00\le30.00[/tex]EXPLANATION
Let the number of slices of pizza that Jess can buy be x.
She has to buy a ticket which costs $12 and x slices of pizza for $2.25 each. All these must cost less than or equal to $30 which Jess has.
Therefore, the inequality that represents how many slices of pizza Jess can buy is:
[tex]2.25x+12.00\le30.00[/tex]Find the average rate of change for the function f(x) = 3x + 10.1.)102.)73.)34.)-3
Answers
To find the average rate of change of f(x) = 3x + 10, simply compare with f(x) = mx + 10 where m is the average rate of change
Comparing the two equation, average rate of change = m = 3
473)1 12206115184 4•2D) -5 units(5.3)(5,-2)In the graph above, what's the distance between (5,-2) and (5, 3)?OA) 5 unitsOB) 1 unitOC) 3 units
Answers
Given:
The given two points are
[tex]\begin{gathered} (x1,y1)=(5,-2) \\ (x2,y2)=(5,3) \end{gathered}[/tex]Required:
To find the distance between the given two points.
Explanation:
The diatnce between the two points is given by
[tex]\begin{gathered} d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\ \\ =\sqrt{(5-5)^2+(3-(-2))^2} \\ \\ =\sqrt{0+5^2} \\ \\ =\sqrt{25} \\ \\ =5 \end{gathered}[/tex]Final Answer:
The option A is correct.
5 units.
In rectangle ABCD, point E lies halfway between sides AB and CD and halfway between sides AD and BC. If AB = 9and BC = 10, what is the area of the shaded region? Write your answer as a decimal if necessary.
Answers
Answer:
45 square units.
Explanation:
Given that point E is halfway between AD and BC; and
• AB=9
,• BC=10
The diagram showing this is attached below:
The unshaded region is divided into two triangles (BEC and AED) each having the dimensions:
• Base = 10
,• Height = 4.5
Therefore, the area of the shaded region will be:
[tex]\begin{gathered} \text{Area of shaded region=Area of Rectangle-Area of Unshaded Region} \\ =(10\times9)-2(\frac{1}{2}\times10\times4.5) \\ =90-45 \\ =45\text{ square units.} \end{gathered}[/tex]The area of the shaded region is 45 square units.
In the accompanying diagram of (triangle) ABC, AB is extended
to D, exterior angle CBD measures 145°, and m(angle)C = 75.
What is mZ CAB?
Answers
Given that:
[tex]m\angle CBD=145^{\circ},m\angle C=75^{\circ}[/tex]Angle ABD is the sum of the angles CBD and CBA. Find angle CBA.
[tex]\begin{gathered} m\angle ABD=m\angle CBD+m\angle CBA \\ 180^{\circ}=145^{\circ}+m\angle\text{CBA} \\ m\angle CBA=180^{\circ}-145^{\circ} \\ =35^{\circ} \end{gathered}[/tex]Use the fact that the sum of the interior angles of a triangle is 180 degrees.
Here the sum of the interior angles of triangle ABC is 180 degrees.
[tex]\begin{gathered} m\angle CAB+m\angle ABC+m\angle BCA=180^{\circ} \\ m\angle CAB+35^{\circ}+75^{\circ}=180^{\circ} \\ m\angle CAB+110^{\circ}=180^{\circ} \\ m\angle CAB=180^{\circ}-110^{\circ} \\ =70^{\circ} \end{gathered}[/tex]The measure of the angle CAB is 70 degrees.
Second option is correct.
Jane has been saving quarters and dimes. She opened up the piggy bank and determined that it contained 35 coins worth $6.80. Determine how many dimes and quarters were in the piggy bank.
Answers
Hello!
First of all, let's write some important information:
• There are 35 coins in total;
,• The total amount is $6.80.
Let's write d for dimes and q for quarters.
Writing the exercise as a linear system, we will have:
[tex]\begin{cases}d+q={35} \\ 0.10d+0.25q={6.80}\end{cases}[/tex]Let's isolate the variable d in the first equation:
[tex]\begin{cases}d+q={35\rightarrow d=35-q} \\ 0.10d+0.25q={6.80}\end{cases}[/tex]Now let's replace it in the second equation:
[tex]\begin{gathered} 0.10d+0.25q=6.80 \\ 0.10(35-q)+0.25q=6.80 \\ 3.50-0.10q+0.25q=6.80 \\ 0.15q=6.80-3.50 \\ 0.15q=3.30 \\ q=\frac{3.30}{0.15} \\ \\ \boxed{q=22\text{ quarter coins}} \end{gathered}[/tex]As we know the number of quarters, we just have to replace it:
[tex]\begin{gathered} d+q=35 \\ d+22=35 \\ d=35-22 \\ \boxed{d=13\text{ dimes coins}} \end{gathered}[/tex]Answer:In the pig bank were 13 dimes coins and 22 quarter coins.
solve for n. n/-5= 7
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We are given the following equation:
[tex]\frac{n}{-5}=7[/tex]To solve for "n" we must multiply both sides of the equation by -5:
[tex]-\frac{5n}{-5}=(7)(-5)[/tex]Solving the operations:
[tex]n=-35[/tex]Therefore, n = -35
Translate the phrase into algebraic symbols.a number x decreased by seventy
Answers
Answer:
x-70
Explanation:
Given the phrase:
'a number x decreased by seventy'
When a number (say x) is decreased by a given value (70), we simply subtract the value from the number.
Therefore, the algebraic symbol for the phrase is:
[tex]x-70[/tex]Which equation has a solution of 3/4 for y?4y = 6y - 1=-1/48y = 92 1/4 + y = 4
Answers
The first tep is to solve each equation for y
For the first equation,
4y = 6
y = 6/4 = 3/2
For the second equation,
y - 1 = - 1/4
y = - 1/4 + 1 = 3/4
For the third equation,
8y = 9
y = 9/8
For the fourth equation,
2 1/4 + y = 4
y = 4 - 2 1/4
y = 1 3/4
Thus, the correct option is
y - 1 = - 1/4
Use the following data set to answer the question below.50 60 8090 50 7040 50 80What is the mode for the data set?
Answers
We have a dataset that is:
50 60 80
90 50 70
40 50 80
We have to identify the mode of this dataset.
The mode is the value in the dataset that has the highest frequency. We can have more than one mode if there is more than one value with the maximum frequency.
To find the mode it is usually helpful to count the frequency for each element.
We can do it as:
50: III
60: I
80: II
90: I
70: I
40: I
As "50" has the highest frequency, with a value of 3, it is the mode of the dataset
Answer: the mode is 50.
Solve the quadratic equation by completing the square. x2 - 12x+34 = 0 First, choose the appropriate form and fill in the blanks with the correct numbers. Then, solve the equation. Round your answer to the nearest hundredth. If there is more than one solution, separate them with commas.
Answers
The answers are x1 = 14.37 and x2 = -2.37
x1 is the positive and x2 is the negative
There are two solutions x1 = 14.37, x2 = -2.37
The equation is y=3x+15/x-2I know that the vertical asymptote is x=2That the horizontal asymptote is y=3By looking at the graph I need to find several points on either side. I’m having difficulty with this
Answers
Given
The equation,
[tex]y=\frac{3x+15}{x-2}[/tex]To find the points in the graph of the given equation.
Explanation:
It is given that,
[tex]y=\frac{3x+15}{x-2}[/tex]That implies, the graph of the above equation is,
Then, the graph of the equation is,
Hi, I started the question with my other tutor but I lost him right when I was figuring out the answer. Please help. Question 3!
Answers
3)
Answer: 54.95 ft^2
Explanation:
The formula for calculating the area of a sector is expressed s
Area = θ/360 x πr^2
where
π is a constant whose value is 3.14
θ is the angle subtended at the center of the circle or the angle o the sector
r is the radius of the circle
From the information given,
r = 15
The total angle in a circle = 360 degrees
θ = 360 - 332 = 28
Area of shaded sector 28/360 x 3.14 x 15^2
Area of shaded sector = 54.95 ft^2
A group of 145 students at an elementary school were asked if they prefer the color orange to the color green. The resultsare shown in the table below. Given that a randomly selected survey participant is a male, what is the probability that thisstudent prefers the color green?
Answers
Notice that there are 52 male students, and 16 of them prefer the color green. Since the survey was applied to 145 students in total,we have that the probability to select a male participant that prefers the color green is:
[tex]P(\text{male,green})=\frac{16}{145}[/tex]Does the table represent a linear function. Can I also get the steps to solving linear and non-linear questions? Thanks!Problem #13
Answers
Given the table
If the slopes of the between the points are same, then it is a linear function.
Consider the two points (-2,0.2) and (0,2). Find the slope using the two point formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]The slope for the points (-2, 0.2 ) and (0, 2) is
[tex]\begin{gathered} m=\frac{2-0.2}{0-(-2)} \\ =0.9 \end{gathered}[/tex]Consider the points (0, 2) and (2, 3.8). The slope for the points (0, 2) and (2, 3.8) is
[tex]\begin{gathered} m=\frac{3.8-2}{2-0} \\ =\frac{1.8}{2} \\ =0.9 \end{gathered}[/tex]Consider the points (2, 3.8) and (4, 5.6). The slope for the points (2, 3.8) and (4, 5.6) is
[tex]\begin{gathered} m=\frac{5.6-3.8}{4-2} \\ =\frac{1.8}{2} \\ =0.9 \end{gathered}[/tex]The slope is same for every consecutive pair of points. Hence the given function is linear.
4.) Divide: 6/28x+4 ÷ 6/35x+5
Answers
Here, we want to make a division
The easiest way to go about this is to turn what we have on the right handside upside down, then change the sign at the middle to multiplication
We have;
[tex]\begin{gathered} \frac{6}{28x\text{ + 4}}\text{ }\times\text{ }\frac{35x\text{ + 5}}{6} \\ \\ =\text{ }\frac{35x\text{ + 5}}{28x\text{ + 4}} \\ \\ =\text{ }\frac{5(7x\text{ + 1)}}{4(7x\text{ + 1)}} \\ \\ =\text{ }\frac{5}{4}\text{ = 1}\frac{1}{4} \end{gathered}[/tex]Describe and correct the error in writing a linear function with the values f (5) =4, g (3) =10
Answers
Given a linear function
please help me find the bearing in this problem, thank you!
Answers
The bearing from O to A is the measure of the angle between the North and The arrow of A
Since the North is perpendicular to the East, then
The angle between N and E is 90 degrees
Then subtract 75 degrees from 90 degrees to find the angle between the North and the arrow of A
[tex]\begin{gathered} B=90^{\circ}-75^{\circ} \\ B=015^{\circ} \end{gathered}[/tex]The bearing from O to A is 015 degrees
Note that we measure the bearing from North to the position clockwise